The generator matrix

 1  0  1  1  1  1  1  1  1  1  1
 0  1  1  2  0  1  2  0  0  0  0
 0  0 2X  0  0  0  0  X  0  X  0
 0  0  0  X  0  0  0 2X  X 2X  0
 0  0  0  0  X  0  0 2X 2X  X  0
 0  0  0  0  0 2X  0 2X 2X 2X  0
 0  0  0  0  0  0  X 2X  X  X  0

generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+30x^9+18x^10+98x^12+144x^13+190x^15+468x^16+1302x^18+864x^19+1458x^20+4382x^21+1152x^22+2916x^23+4360x^24+1152x^25+368x^27+576x^28+164x^30+40x^33

The gray image is a linear code over GF(3) with n=33, k=9 and d=9.
This code was found by Heurico 1.16 in 0.0883 seconds.